Polynomial automorphisms of C^n preserving the Markoff-Hurwitz polynomial

Abstract

We study the action of the group of polynomial automorphisms of C^n (n>2) which preserve the Markoff-Hurwitz polynomial H(x):= x_1^2 + x_2^2 + ... + x_n^2 - x_1 x_2 ... x_n. Our main results include the determination of the group, the description of a non-empty open subset of C^n on which the group acts properly discontinuously (domain of discontinuity), and identities for the orbit of points in the domain of discontinuity.

arXiv commentdedicatory added, grant support acknowledged, minor corrections, references updated

References in corpus (2)

• The Modular Group Action on Real SL(2)-characters of a One-Holed Torus
• Simple geodesics and Markoff quads

Cited by in corpus (3)

• McShane identities for Higher Teichmüller theory and the Goncharov-Shen potential
• Birational Kleinian groups
• On the character variety of the three-holed projective plane